Executive Summary
Following recent policy changes regarding International Student enrolment requirements, the client requires a forecasting model to estimate student enrolments and confirm the University’s budget before the Census date. A linear model was created for each faculty, considering the different fee types, years and semesters and the COVID-19 impact from 2020 to 2021. Based on the 2024 linear model predictions, the University is expected to reach budget. However, training the linear model with additional historical data (including consideration of additional variables) is recommended to improve the model’s accuracy.
Background
In 2024, the Australian government implemented policy changes for international students at tertiary education institutions designed to enhance the quality of education and reinforce the integrity of the visa system. A key aspect of these changes is that international fee-paying students are no longer mandated to enrol for both Semester 1 and Semester 2 during the initial enrollment period of Semester 1. This shift moves away from the traditional requirement for international students to commit to a full academic year upfront.
This policy adjustment will influence how international students approach their education in Australia. This change may result in more fluctuating enrollment figures from one semester to the next, posing a challenge for the University of Sydney regarding planning and resource allocation.
CSP (Commonwealth Supported Places): A funding scheme where the Australian government subsidises the tuition fee of students at Australian universities. This support is only available to domestic students.
DFEE (Domestic Fee-Paying Students): Students who do not qualify for Commonwealth support and must pay full tuition fees. These fees are typically higher than those for Commonwealth Supported Places.
IFEE (International Fee-Paying Students): Students from countries other than Australia who attend Australian universities. These students pay full tuition fees, which are usually higher than the fees for domestic students.
EFTSL (Equivalent Full-Time Student Load): A measure used to indicate the standard annual full-time study load. One EFTSL is typically equivalent to one year of full-time study. This measure is used to calculate the study load of part-time students in proportion to a full-time study load.
Client’s Aims
The client requires a forecasting model that can be employed early in the academic year—specifically, pre-census in January or February. This model is intended to provide a reliable preliminary estimate of the entire year’s enrolment figures. It must also adapt to recent policy changes that have eliminated the requirement for international students to enrol for both semesters at the start of the academic year.
Data
The provided data, including EFTSL values for 2018-2023, has been plotted below. Most faculties generally show a relatively stable trend in EFTSL over this period. In the Faculty of Engineering and Business School, EFTSL is significantly higher for international students. For Sydney Law School, Faculty of Science, Sydney Conservatorium of Music, and Faculty of Medicine and Health, CSP students account for the majority of EFTSL. The Faculty of Arts and Social Sciences has seen IFEE EFTSL overtake CSP since midway through 2020.
Forecast Modelling
A linear model has been created to forecast equivalent full-time study load (EFTSL) for each major Faculty (Faculty of Arts and Social Sciences, Business School, Faculty of Engineering, Faculty of Medicine and Health, Faculty of Science, Sydney School of Architecture, Design and Planning, Sydney Law School and Sydney Conservatorium of Music) within the University. Predicting EFTSL allows for flexibility of the model with variance of University Fees for each faculty and accounts for the varied study load of each student. For each linear model, Fee Type, Year and Semester are considered. A dummy variable was also added to consider the impact of the COVID-19 pandemic on EFTSL.
Assumptions of linear modelling include linearity, homoscedasticity, independence, and normality. Given that each of the data points is independent due to being separated across Semester, Year, Fee Type, and Faculty and has a linear relationship, these assumptions have been met. Further diagnostic plots to demonstrate this can be found in the Appendix (Section 7).
A general summary for each model is tabulated below in Table 1, and the coefficients of each model are in Table 6. A model was created for each combination of faculty and fee types, resulting in a total of 24 models.
| Faculty of Teaching | Fee Type | R-Squared | Adjusted R-Squared | P-Value | AIC | Corrected AIC |
|---|---|---|---|---|---|---|
| Business School | CSP | 0.92 | 0.89 | 0.00 | 87.30 | 97.30 |
| Business School | DFEE | 0.05 | −0.31 | 0.94 | 94.27 | 104.27 |
| Business School | IFEE | 0.34 | 0.09 | 0.32 | 150.58 | 160.58 |
| Faculty of Arts and Social Sciences | CSP | 0.91 | 0.88 | 0.00 | 110.24 | 120.24 |
| Faculty of Arts and Social Sciences | DFEE | 0.43 | 0.21 | 0.19 | 87.66 | 97.66 |
| Faculty of Arts and Social Sciences | IFEE | 0.88 | 0.84 | 0.00 | 141.76 | 151.76 |
| Faculty of Engineering | CSP | 0.89 | 0.85 | 0.00 | 88.41 | 98.41 |
| Faculty of Engineering | DFEE | 0.55 | 0.39 | 0.08 | 62.19 | 72.19 |
| Faculty of Engineering | IFEE | 0.90 | 0.86 | 0.00 | 120.59 | 130.59 |
| Faculty of Medicine and Health | CSP | 0.35 | 0.10 | 0.31 | 115.49 | 125.49 |
| Faculty of Medicine and Health | DFEE | 0.45 | 0.24 | 0.17 | 101.17 | 111.17 |
| Faculty of Medicine and Health | IFEE | 0.10 | −0.24 | 0.83 | 102.21 | 112.21 |
| Faculty of Science | CSP | 0.88 | 0.84 | 0.00 | 102.56 | 112.56 |
| Faculty of Science | DFEE | 0.81 | 0.74 | 0.00 | 53.62 | 63.62 |
| Faculty of Science | IFEE | 0.94 | 0.91 | 0.00 | 108.14 | 118.14 |
| Sydney Conservatorium of Music | CSP | 0.88 | 0.83 | 0.00 | 76.28 | 86.28 |
| Sydney Conservatorium of Music | DFEE | 0.84 | 0.78 | 0.00 | 20.61 | 30.61 |
| Sydney Conservatorium of Music | IFEE | 0.89 | 0.85 | 0.00 | 47.14 | 57.14 |
| Sydney Law School | CSP | 0.59 | 0.43 | 0.06 | 82.64 | 92.64 |
| Sydney Law School | DFEE | 0.76 | 0.67 | 0.01 | 70.57 | 80.57 |
| Sydney Law School | IFEE | 0.92 | 0.90 | 0.00 | 73.92 | 83.92 |
| Sydney School of Architecture, Design and Planning | CSP | 0.96 | 0.95 | 0.00 | 63.97 | 73.97 |
| Sydney School of Architecture, Design and Planning | DFEE | 0.25 | −0.03 | 0.49 | 61.54 | 71.54 |
| Sydney School of Architecture, Design and Planning | IFEE | 0.96 | 0.95 | 0.00 | 86.96 | 96.96 |
R-Squared: This value tells us how well our model’s predictions match the actual data. A higher R-Squared value means a better fit.
Adjusted R-Squared: This is a tweaked version of R-Squared that adjusts for the number of predictors used in the model. It provides a more accurate score by considering the complexity of the model. Like R-Squared, a higher value indicates a better fit, but it is generally more reliable especially when comparing models with different numbers of predictors.
P-Value: This number helps us determine whether the results of our analysis are statistically significant. In simple terms, it tests the probability that the relationships observed in your data occurred by chance. A smaller P-Value (typically less than 0.05) suggests that the findings are significant and not just a random occurrence.
AIC (Akaike Information Criterion): This is a tool we use to compare different models. It balances the model’s complexity against how well it fits the data. A lower AIC value indicates a model that better fits the data without becoming overly complex.
Corrected AIC (AICc): This is a version of AIC adjusted for smaller sample sizes. It’s particularly useful when you have a large number of parameters relative to the number of observations. Like AIC, a lower AICc value suggests a better model.
Estimates For Each Coefficients
The chart below represents how various factors affect university fees. It breaks down the influence of different variables like the year, the second semester, and COVID-19 for each department.
Semester 1 was kept as a baseline. This means that when predictions are made for the first semester, the model will only consider the year and the impact of COVID-19. This method helps us focus on what changes, rather than what stays the same.
Similarly, for the COVID-19 impact variable, the default is that there is no COVID-19 impact. This means that when predictions are made for future years, the model doesn’t include it in it’s forecast.
For CSP, EFTSL is lower in Semester 2 across all Faculties. The Business School and Faculty of Science have the largest decrease in EFTSL in Semester 2, while compared to other Faculties this negative impact is minimal in the Sydney School of Architecture, Design and Planning. With every increase in Year, EFTSL is increasing in the Faculty of Medicine and Health, Engineering, the Sydney School of Architecture, Design and Planning and Sydney Conservatorium of Music. EFTSL decreases most every year in the Faculty of Arts and Social Sciences. COVID-19 increased EFTSL in all Faculties except for the Faculty of Medicine and Health, where it had a negative impact.
For DFEE, EFTSL is lower in Semester 2 across all Faculties except the Business School. The Faculty of Medicine and Health has the largest decrease in EFTSL in Semester 2. As the Year increases, EFTSL increases in the Faculty of Medicine and Health, Business School and Sydney School of Architecture, Design and Planning. The Faculty of Arts and Social Sciences and Sydney Law School have the largest decrease in EFTSL with every increase in Year. COVID-19 increased EFTSL in all Faculties except the Sydney Conservatorium of Music.
For IFEE, EFTSL is higher in Semester 2 across all Faculties with the exception of Faculty of Medicine and Health and Sydney Conservatorium of Music (by a very small amount). The largest increases in Semester 2 EFTSL occur in the Faculty of Arts and Social Sciences, Business School and Faculty of Engineering. With increases in Year, EFTSL increases in all Faculties, by the highest amount in the Faculty of Arts and Social Sciences, followed by the Faculty of Engineering and Faculty of Science. COVID-19 had a positive impact on EFTSL in the Business School, Faculty of Arts and Social Sciences and Faculty of Science.
Backcasting
Using the linear model, it is possible to compare predictions of EFTSL for previous years, which can be compared with data to demonstrate the model’s performance.
Forecasting
The forecasting plots below demonstrate EFTSL forecasts for the next five years. Evidently, from the graphs, the model tends to make a large jump in EFTSL estimations. This is likely due to the extrapolation (estimating for larger values than what the data is trained on) occurring here.
Performance
Given the relatively small amount of training data (5 years) from which the model has been created, the model is somewhat limited. In particular, the model has been overfitted, meaning that the model cannot accurately extrapolate (estimate values for Years outside of the range of Years on which it was trained) and will continue to predict trends that match those in the training data. Due to the nature of the problem, which involves a change in trends of behaviour concerning Semester 2 enrolments there may be additional changes that the model is not accounting for.
Mean Absolute Error (MAE)
We used a method called Mean Absolute Error (MAE) to evaluate how well our forecasting model performed. This method measures the accuracy of our predictions by calculating the average difference between the predicted student enrollments (EFTSL) and the actual enrollments recorded in 2023. The differences are taken as absolute values, which means we focus only on the size of the errors without considering whether the predictions were too high or too low.
Our results showed that the MAE for our model was higher than the MAE for the existing forecasts. This suggests that our model’s predictions were generally further from the actual numbers than the existing forecasts. The larger MAE indicates that our model was less accurate, meaning our predictions about student enrollment were not as close to the actual figures as those of the existing forecasts.
This is likely due to the small size (\(n = 5\) years) of the data from which the model was built, as well as our model’s inability to account for additional factors of variability in EFTSL compared to the existing model.
| Faculty of teaching | Fee Type | Linear Model MAE | Existing Forecast MAE |
|---|---|---|---|
| Business School | CSP | 20.93 | 26.00 |
| Business School | DFEE | 28.76 | 6.06 |
| Business School | IFEE | 256.36 | 475.57 |
| Faculty of Arts and Social Sciences | CSP | 51.31 | 32.52 |
| Faculty of Arts and Social Sciences | DFEE | 21.13 | 4.62 |
| Faculty of Arts and Social Sciences | IFEE | 184.89 | 72.13 |
| Faculty of Engineering | CSP | 21.70 | 14.38 |
| Faculty of Engineering | DFEE | 7.00 | 3.59 |
| Faculty of Engineering | IFEE | 81.17 | 27.55 |
| Faculty of Medicine and Health | CSP | 69.36 | 15.18 |
| Faculty of Medicine and Health | DFEE | 38.67 | 10.01 |
| Faculty of Medicine and Health | IFEE | 43.59 | 8.80 |
| Faculty of Science | CSP | 39.26 | 18.61 |
| Faculty of Science | DFEE | 5.29 | 2.28 |
| Faculty of Science | IFEE | 44.57 | 15.91 |
| Sydney Conservatorium of Music | CSP | 12.77 | 7.18 |
| Sydney Conservatorium of Music | DFEE | 1.29 | 0.32 |
| Sydney Conservatorium of Music | IFEE | 3.43 | 1.29 |
| Sydney Law School | CSP | 18.15 | 8.68 |
| Sydney Law School | DFEE | 9.70 | 6.28 |
| Sydney Law School | IFEE | 12.24 | 6.76 |
| Sydney School of Architecture, Design and Planning | CSP | 7.71 | 3.58 |
| Sydney School of Architecture, Design and Planning | DFEE | 6.86 | 1.21 |
| Sydney School of Architecture, Design and Planning | IFEE | 21.11 | 3.90 |
Percentage Change
Percentage change was also investigated to compare the existing forecast and the linear model. Examining differences in percentage change shows that the model performs most accurately with the CSP and IFEE types. There is a large variance in the DFEE percentage change values, most likely due to the small data available for DFEE students. However, given recent policy changes, the highest priority is to predict IFEE students, so this variance in DFEE is not of great importance.
Table 3: EFTSL Percentage Change
| Faculty of Teaching | CSP | DFEE | IFEE |
|---|---|---|---|
| Business School | -0.7276 | 0.7144 | 2.0845 |
| Faculty of Arts and Social Sciences | -1.9400 | -4.9496 | 6.8222 |
| Faculty of Engineering | 1.5220 | -2.7069 | 4.4429 |
| Faculty of Medicine and Health | 0.1768 | 0.2945 | 0.7948 |
| Faculty of Science | -0.6972 | -6.1094 | 5.8540 |
| Sydney Conservatorium of Music | 1.8246 | -6.5335 | 3.9446 |
| Sydney Law School | -1.2799 | -4.5235 | 4.7425 |
| Sydney School of Architecture, Design and Planning | 2.4782 | -0.5129 | 5.8456 |
| Faculty of Teaching | CSP | DFEE | IFEE |
|---|---|---|---|
| Business School | -0.9877 | 2.1725 | 8.4459 |
| Faculty of Arts and Social Sciences | -2.3069 | -4.5317 | 6.5422 |
| Faculty of Engineering | 1.2167 | -3.0673 | 4.3133 |
| Faculty of Medicine and Health | -0.0190 | 0.2968 | 0.6242 |
| Faculty of Science | -0.6634 | -5.5898 | 6.0633 |
| Sydney Conservatorium of Music | 1.5412 | -5.8873 | 3.9948 |
| Sydney Law School | -1.0863 | -4.1787 | 5.2968 |
| Sydney School of Architecture, Design and Planning | 2.5530 | -1.1530 | 5.7149 |
| Faculty of Teaching | CSP | DFEE | IFEE |
|---|---|---|---|
| Business School | -1.0763 | 1.3769 | 1.8731 |
| Faculty of Arts and Social Sciences | -1.7139 | -2.7046 | 6.8425 |
| Faculty of Engineering | 1.2508 | -1.9878 | 4.0756 |
| Faculty of Medicine and Health | 0.2978 | 1.1331 | -0.0387 |
| Faculty of Science | -0.3787 | -5.3869 | 5.3839 |
| Sydney Conservatorium of Music | 2.2046 | -4.7458 | 4.6665 |
| Sydney Law School | -0.8340 | -3.6006 | 4.2388 |
| Sydney School of Architecture, Design and Planning | 2.2230 | 1.1343 | 5.5214 |
Comparison to Existing Forecast
In addition to comparing percentage change across the linear model and existing forecast, the two calculated values can be compared graphically for each Faculty, as seen below in Figures 21-28.
Visually, the estimated values appear relatively similar across both models, with the exception of EFTSL for IFEE Business School in 2019-2021. The estimates of the Linear Model are more consistent than the Existing Forecast model, which is intuitive given its linear nature, while the existing forecast model may take in account more external factors which would explain more unpredictable trends in estimate values.
Budget
Regarding the client’s concerns about meeting budget, the linear model forecasts an overall income of $2,416,435,480 across the major faculties of the University of Sydney in 2024. The split of this income across Faculties can be seen in Table 4 below.
This exceeds the budgets of the previous years, supporting the University’s on-track meeting of the budget for 2024.
| Faculty of Teaching | EFTSL | Income (AUD$) |
|---|---|---|
| Business School | 11,581.559 | 545,770,788 |
| Faculty of Arts and Social Sciences | 14,949.297 | 571,100,838 |
| Faculty of Engineering | 8,516.052 | 378,804,089 |
| Faculty of Medicine and Health | 9,859.530 | 383,259,225 |
| Faculty of Science | 8,033.494 | 311,997,256 |
| Sydney Conservatorium of Music | 1,229.235 | 33,754,546 |
| Sydney Law School | 2,053.922 | 74,482,452 |
| Sydney School of Architecture, Design and Planning | 3,133.096 | 117,266,286 |
| Total | 59,356.185 | 2,416,435,480 |
Conclusion
By constructing a linear model, EFTSL forecasting within each major Faculty of the University of Sydney has become possible. While this model does not perform as well as the existing forecast method, it has the potential for significant improvement with additional hisotrical data for training and consideration of factors influencing student enrolment that were not available in the initial dataset. With these enhancements, the model can further aid in forecasting enrolments from International Students in light of recent policy changes. However, it is important to consider such policies will lead to new behaviours in student enrolment and the current model is based on old behaviours so there may be further changes unaccounted for by the model. Nevertheless, based on the results of the linear model, the University of Sydney is on track to meet its budget for 2024.
Appendix
A. Fees per EFTSL in each Faculty
| Faculty of teaching | CSP | DFEE | IFEE |
|---|---|---|---|
| Faculty of Arts and Social Sciences | 18,753.57 | 32,546.67 | 50,759.61 |
| Business School | 17,631.13 | 42,939.24 | 54,844.02 |
| Faculty of Engineering | 25,713.36 | 39,625.79 | 53,942.01 |
| Faculty of Medicine and Health | 29,687.77 | 44,444.43 | 58,892.39 |
| Faculty of Science | 25,905.67 | 39,182.93 | 55,778.32 |
| Sydney School of Architecture, Design and Planning | 23,867.44 | 30,095.07 | 47,220.94 |
| Sydney Law School | 17,239.20 | 41,322.73 | 55,219.47 |
| Sydney Conservatorium of Music | 23,576.27 | 33,635.10 | 48,126.68 |
B. Coefficients for each Linear model
| Faculty of Teaching | Fee Type | Intercept | Year | Semester 2 | COVID-19 Impact |
|---|---|---|---|---|---|
| Business School | CSP | 35535 | -17 | -130 | 103 |
| Business School | DFEE | -3786 | 2 | 12 | 5 |
| Business School | IFEE | -225383 | 114 | 216 | 246 |
| Faculty of Arts and Social Sciences | CSP | 235613 | -115 | -49 | 141 |
| Faculty of Arts and Social Sciences | DFEE | 20183 | -10 | -5 | 29 |
| Faculty of Arts and Social Sciences | IFEE | -759203 | 377 | 297 | 38 |
| Faculty of Engineering | CSP | -80252 | 40 | -58 | 4 |
| Faculty of Engineering | DFEE | 6288 | -3 | -7 | 16 |
| Faculty of Engineering | IFEE | -345143 | 172 | 89 | -34 |
| Faculty of Medicine and Health | CSP | -49735 | 26 | -45 | -67 |
| Faculty of Medicine and Health | DFEE | -43739 | 22 | -20 | 22 |
| Faculty of Medicine and Health | IFEE | -988 | 1 | -11 | -30 |
| Faculty of Science | CSP | 754 | 1 | -226 | 133 |
| Faculty of Science | DFEE | 14640 | -7 | -7 | 3 |
| Faculty of Science | IFEE | -268150 | 133 | 28 | 33 |
| Sydney Conservatorium of Music | CSP | -45054 | 23 | -30 | 18 |
| Sydney Conservatorium of Music | DFEE | 3615 | -2 | -1 | -4 |
| Sydney Conservatorium of Music | IFEE | -13249 | 7 | -3 | -14 |
| Sydney Law School | CSP | 10225 | -5 | -33 | 35 |
| Sydney Law School | DFEE | 25185 | -12 | -7 | 12 |
| Sydney Law School | IFEE | -58010 | 29 | 1 | -18 |
| Sydney School of Architecture, Design and Planning | CSP | -50922 | 25 | -5 | 35 |
| Sydney School of Architecture, Design and Planning | DFEE | -2205 | 1 | -5 | 8 |
| Sydney School of Architecture, Design and Planning | IFEE | -141809 | 71 | 18 | -20 |